You shouldn't have to make this decision alone. The team of health care professionals working with her can give you advice and counsel. The physical therapists (PT) will be measuring her strength, coordination, balance, and motion. These are the skills needed for everyday activities of walking, climbing stairs, and getting around safely.
The occupational therapist (OT) will know when she is ready to resume her daily activities of daily independently in her own home setting. Usually the PT and/or the OT make a home visit and assess her needs based on her living situation. If there is no PT or OT, then a nurse or social worker may be the one to do this.
For example, is her home on one level? Or does she have to manage stairs to get in and out of the house? Are there grab bars in the bathroom to help her manage toileting and bathing? Is the laundry room accessible? What other adaptive aids or equipment are needed for her to bathe, cook, clean, and manage her daily tasks?
The PT can give your mother several tests of physical function to help guide this decision. For example, the Timed Up & Go Test (TUGT) measures how fast a person can get up from a chair, walk three meters, turn and return to sit in the chair. Or patients are given the Six-Minute Walk Test. They walk as far as they can safely in six-minutes.
There are standard measures of how fast a person should be able to do these tasks to show they can live safely by themselves. Your mother's score will be compared to those standards to give you both an idea of how well she is doing.